Rewrite as a simplified fraction. ${2.7\overline{52} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2752.5252...\\ 10x &= 27.5252...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2725}$ ${x = \dfrac{2725}{990}} $ ${x = \dfrac{545}{198}} \text{or} {2 \dfrac{149}{198}}$